When we cbet bluffing, should we focus on how my range hit the flop or how the flop hit my opponent range?

Let's say the flop is 732r. This flop missed both pre flop raiser and my opponent range. So, should we make a cbet on this board?

Any advice would be appreciated!

I think you should look at the range versus range equities.

You picked a great spot to actually 'play' poker here. You need to consider 'everything' once the Flop comes out and now are moving forward under that assumption that the Flop missed both players.

1) What is your perceived range (and image) by V?
2) How wide or narrow is your V's calling range PF when compared to #1?
3) Do you have position?

I think the size of any bet here can throw a huge wrench into the hand flow as well since a larger bet on this kind of board should look more bluffy/weak by a lot of V. What are you afraid of? Why aren't you betting for value?

Medium to small bets may send a different message.

C-bets aren't automatic anymore!! So you are wise to think about these spots when it comes to value, balance, ranging, giving free cards and bluffing. Each bet you place tells a story and you need to make sure that the story is sending a believable message to your opponent whether for value or to generate a fold. GL

OH ... and PS .. sometimes your opponent just gives up. Which is why you will see 'a lot' of Flop bets in tournaments that are actually smaller than the PF raise amount.

This is a good response and I agree that sizing is critical.

Another thing to keep in mind is your opponent's position. Let's say we raise 4BB in position and we get 1 caller. Was this caller in BB or did he limp first from MP?

Now, flop comes out 732r and it checks to you. In which situation would you rather bet? BB completing range vs MP limping range is totally different.

So, I think Villain's range is much more important to consider.

However, just because we missed flop doesn't mean we are bluffing. We can c'bet here with AJs+ and still feel like we are a favorite to win the hand.

Both, if that's not obvious.
If villain has a higher folding frequency on some textures, you can include more bluffs in your range, but he won't fold at a high frequency if he's good enough to realise that you're not repping very much; he'll re-bluff and win the leveling war. (A semi-decent player with a HUD that sees you c-betting too often overall is going to check-raise 743r at a pretty high frequency, because he knows you have so much air in your range).

Since most players at the lowest stakes are level one thinkers that only consider how their own hand hit the flop, you can still get away with exploiting them on dry boards by bluffing more than is optimal in theory. e.g. Villains at 5NL still fold on K72r, Q82r, A93r way more than they really should, so you can still keep betting those with total air until you meet resistance.

If V check raise me on 843r too often. V is not repping very much too. So should we adjust by only value cbet on 843r and stop cbet bluffing. Or should we keep cbet our total air but not fold to V check raise(re-raise or float).

Both. Against someone that x-raises frequently you should c-bet at a lower c-bet frequency with a stronger range that contains enough hands to continue vs check-raises. You also need to defend pretty light vs the check-raises to prevent villain exploiting you by x-raising and picking up the pot with random air. You don't have to eliminate bluffs from your c-betting range, but you want to make it so that you don't fold too often when villain plays back at you.
This is kind of how we get towards theoretically optimal play. By not being too unbalanced when we bet, we can't get exploited by our opponent. If we're too value-heavy or too bluffy, then villain can exploit us.

Note that villains in the micros won't exploit your unbalanced play very much. Indeed, you can maximise your EV by exploiting their imbalances. i.e. If they fold too much, bluff the hell out of them. If your opponent is a very strong player, you need to be more balanced, which would mean not bluffing too much when you rep nothing, and not folding so often when he's capable of raising with air.

As an example of how wide you might have to defend vs a check-raise in theory...
You open OTB and BB defends. You bet 1/2 pot with about 90% of your range on K72r. If villain check-raises 1/2 pot, then it's probably correct for you to call (or 3-bet) with hands as bad as J8s. Almost no one is capable of floating a check-raise with jack high on that board, which is why the BB should be x-raising that dry flop a lot more than most people actually do.
To put it another way, which shows what a leveling war poker can be... villain knows you have a lot of air when you c-bet on K72r, so he expects you to fold to check-raises, but when he check-raises, you can't fold at an exploitably high frequency, because you know he has a lot of trash in his range. So you need to call with some of your really bad hands, and they might be as weak as J8s. If you're not comfortable calling the check-raise with lots of bad hands against a frequent check-raiser, don't bet those bad hands in the first place. Bet at a lower frequency and with hands that can more comfortably continue if they get raised.

I want to re-emphasise that all this theoretical stuff isn't very useful in the micros. Just play some hands and work out the tendencies (i.e. folding frequencies) of your player pool and exploit those tendencies.

2 simple guidelines

Connected medium boards hit caller the most. Even if our range is strong here, we need to take this into consideration, and not just bluff very wide because the board hits our range as well.
Low boards are good for pre-flop raiser, because we have all the overpairs. A-hi K-hi dry boards are good as well, because we have AK AQ and KQ in our range.

You can think of board textures in a spectrum. On the other side you have those very connected medium boards, i.e JT9 with a flush draw. On the other side of the spectrum you have something like A72 rainbow or A33 rainbow. The rest of the board textures follow somewhere in between the spectrum.

Just in general, 732r boards are pretty bad to cbet bluff as the pfr. Everyone assumes you have AK and are going to call any pair in this situation at entry level play.

+10 the info in this thread!

If I may throw a wrench into this garage, does it all change drastically if we aren't playing online micros, but instead a major live tourney? or just a live tourney in general? I know cash and tourney have a totally different enigma, so wanted to know what yalls thoughts were...?

I know how broad of a question this is, where so many factors play a part in this like which level of the tourney we are in, stack sizes, etc. but asking just in general as OP

yes

You should definitely focus on both your range and your opponents range. Your decision to cbet will be based upon the board texture, both of your ranges, and villains tendencies. As always, Poker is very situational.

Personally, I think it is beneficial to think about your overall cbetting strategy in general. Some people will say this is a good flop to cbet because it is dry and your opponent can't have much. Some will say it is bad because this flop misses the hands you should be raising and villain never folds a made hand. I think this is a bit trivial and if you think about the flop and your betting strategy in terms of ranges, you'll have a better understanding of what you are doing. First, I think you should focus on the hands you could have here that you are betting with.

For instance, you'll be betting some of your weaker Ax like A5 and A4, 22, some of your 33, 44-66, some of your 45 and 89, 78, 79, 67, over pairs like 88-TT and half of your JJ+ (you want to bet the ones without backdoor flush draw blockers). So when you do bet this flop, you should mostly be betting for value with only some bluffs mixed in. Most of your other hands you will be checking back like half of your JJ+, A2, A3, maybe A7 so you don't fold out villains Ace high hands, 77 because you're blocking most of villains top pairs (can't have many in the first place), and then a bunch of your air.

So in theory you really don't have many bluffs on this board thus you don't have much of a reason to cbet bluff. When we bet, it's almost always for value and protection. And we mix up some check backs in order to let villain catch up to gain value on a later streets since villain should have so little equity on thus board.

Once you understand how both of your ranges hit this board and figure out a strategy for playing this board, you can adjust to villains tendency. Is villain folding too much? Then cbet bluff more with the air that was checking back. Is villain calling too much? Take some of the value hands you check back with and bet more with them.

The same concept will apply in any form of nlhe, whether it be MTTs or Microstakes cash. The difference is that you can deviate from your initial cbetting strategy in certain situations according to villains tendencies. For instance, in an MTT when you are close to the bubble and stacks are shallow, you can cbet bluff more against players who are clearly playing scared.